1. Field of the Invention
The present invention relates to radar or sonar imaging systems and, more particularly, pertains to a new and improved method for enhancing the resolution of active systems such as synthetic aperture radar (SAR) or synthetic aperture sonar (SAS) images or of passive systems such as sensor array sonar images, by means of high-order measurements for autofocus processing.
2. Description of Related Art
Radar is an important sensor technology because it provides an all-weather, day or night capability to detect or locate objects and to generate a spatial, visual representation of the electromagnetic reflectivity of an illuminated scene. Imaging radar provides a two-dimensional representation of scatterers (objects of interest) in the illuminated scene that contains detailed information with fine spatial resolution in the range and cross-range (or azimuth) directions. A large antenna aperture is required in conventional imaging radar systems to achieve a narrow beamwidth and, consequently, fine azimuth resolution. Practical constraints on antenna size have led to the introduction of synthetic aperture radar (SAR) as an alternative means for improving azimuth resolution by synthesizing pulse-to-pulse return signals collected by a moving platform with a small antenna. The signal synthesis from many successive locations of the moving platform can accomplish what would otherwise require a larger antenna aperture.
Normal SAR data collection requires phase coherence, not only within each pulse for range resolution, but also from pulse to pulse over the collection time needed for azimuth resolution. The platform position affects the pulse-to-pulse phase coherence over the synthetic aperture. The platform position history includes both planned changes and unplanned perturbations of the antenna location. Extraneous platform motion creates phase effects in the SAR signal history that the autofocus processor must cancel in order to maintain phase coherence and achieve good image quality. To use the synthetic aperture concept for generating fine azimuth resolution in radar imagery, the SAR system must account for the distance from the target to the radar antenna at the transmission time of each radar pulse. For airborne SAR, an inertial navigation system (INS) and possibly a global positioning system (GPS) receiver are onboard the SAR platform to measure its relative position and motion. The needed information can also be obtained from the received radar signals themselves. This approach involves measuring the effects of the motion (phase errors) without explicitly measuring the associated motions. Various autofocus techniques are based on measuring phase errors only. Autofocus techniques currently used improve image clarity by alleviating phase errors present after conventional motion compensation and image formatting procedures. Autofocus with respect to SAR or SAS imaging is the computer-automated estimation and subsequent removal of these phase errors. In SAR, these techniques may replace motion measurement entirely or they may simply be an adjunct to actual motion measurements.
In passive systems such as in sensor array sonar that utilize multiple sensors displaced from each other in water, the water medium tends to phase distort the wavefront being received by the sensor array creating a similar phase error problem as encountered in SAR and SAS imaging systems.
For a spotlight radar system, the model for the azimuthal signal g(x) over the synthetic aperture duration T.sub.a from a single range bin is: ##EQU1## where a .omega..sub.0, and .phi..sub.0 represent the magnitude, frequency, and phase of signal history, respectively; and .phi..sub.e (x) is the phase error present in the signal history.
When the phase error term is a quadratic polynomial, conventional methods to estimate or compensate the phase error include the mapdrift (MD) algorithm and the phase difference (PD) algorithm which found significant application in early fine-resolution imaging radars. See W. G. Carrara, R. S. Goodman, and R. M. Majewski, Spotlight Synthetic Aperture Radar: Signal Processing Algorithms, Artech Hose, Boston, 1995. However, applicability of these algorithms is limited to correction of a quadratic phase error which cannot be considered a general model for all phase errors. Extension of the MD algorithm to estimate phase errors of a higher degree (than quadratic) is possible by dividing the signal history aperture into more than two subapertures. In general, N subapertures are adequate to estimate the coefficients of an Nth-order polynomial error model. See C. E. Mancill and J. M. Swiger, "A Map Drift Autofocus Technique for Correcting Higher Order SAR Phase Errors," 27th Annual Tri-Service Radar Symposium Record, Monterey, Calif., June, 1981.
The phase gradient autofocus (PGA) algorithm is currently the leading algorithm for estimating higher degree phase errors. See U.S. Pat. No. 4,924,229, P. H. Eichel, D. C. Ghiglia, and C. V. Jakowatz, "Phase Correction System for Automatic Focusing of Synthetic Aperture Radar," May 8, 1990. The algorithm is not model-based and its implementation does not require explicit selection of a maximum degree for the model of the phase error being estimated. The PGA algorithm is accepted as the state of the art for autofocus processing in a general context (higher degree). The PGA algorithm evaluates the derivative g.sub.0 (x) of the azimuthal signal g.sub.0 (x), which is computed from g(x) after appropriate frequency shifting by .omega..sub.0 and windowing (application of weighting functions) in the frequency domain. Since: EQU g.sub.0 (x)=j.phi..sub.e (x)g.sub.0 (x) (2)
where .phi..sub.e (x) is the time derivative of the phase error, we can estimate .phi..sub.e (x) using the computed values of g.sub.0 (x) and the measured values g.sub.0 (x) as: ##EQU2## where g.sub.0 *(x) is the complex conjugate of g.sub.0 (x). Integration of the phase error gradient estimate .phi..sub.e (x) provides the phase error estimate .phi..sub.e (x) to within a constant. The phase error gradient is usually estimated over several range bins. To obtain satisfactorily good image quality, one has to apply the PGA algorithm iteratively with some effective criterion for terminating algorithm iteration, e.g., a pre-assigned threshold value applied to the mean-square value of the estimated phase error at each iteration.
To focus a SAR image, the prior art estimates and compensates the phase error iteratively. Also, the derivative computation of a discrete-time signal (with or without FFT) is very sensitive to additive noise. The present invention, on the other hand, achieves SAR, SAS, and sensor arrays image autofocusing without iterative processing, by using high-order measurements and a computationally efficient process. Furthermore, derivative terms that can be a source of significant estimation errors in the presence of noise in the data are not used.